Isabel Demongodin

Differential Petri nets: representing continuous systems in a discrete-event world

Differential Petri nets are a new extension of Petri nets. Through the introduction of the differential place, the differential transition, and suitable evolution rules, it is possible to model concurrently discrete-event processes and continuous-time dynamic processes, represented by systems of linear ordinary differential equations. This model can contribute to the performance analysis and design of industrial supervisory control systems and of hybrid control systems in general.

Max-Plus Control Design for Temporal Constraints Meeting in Timed Event Graphs

The aim of the presented work is the control of Timed Event Graph to meet tight temporal constraints. The problem of temporal constraints is formulated in terms of control of linear Max-Plus models. First, the synthesis of a control law that ensures the satisfaction of a single constraint for a single input system is presented. Then, the single input multi-constraints problem is tackled and finally, the method is extended to the multi-inputs, multi-constraints problem. The proposed method is illustrated on the example of a simple production process.

Control of Linear Min-plus Systems under Temporal Constraints

We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a system of difference equations that are linear in the Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the min-plus algebra. Then, a method for the synthesis of a control law ensuring the respect of constraints is described. We give explicit formulas characterizing a control law, which, if two conditions are satisfied, ensures the validity of the temporal constraints. It is a causal state feedback, involving delays. The method is illustrated on an example.

Fundamental concepts of analysis in batches Petri nets

This paper presents the structural analysis concepts of batches Petri net, a discrete-continuous model for mixed production system. After some recalls on the batches Petri net class, we provide the fundamental equations that govern the dynamic behavior, define the invariant concepts with the determination of the quantity vector, and finally, analyze the structural properties through an example.

Modelling of high throughput production lines by using generic models described in batches Petri nets

In order to optimise high throughput production lines, modelling of the physical part must be carried out to simulate these production lines. In this note, modelling, using generic models which each represents a behaviour described in batches Petri nets, is presented. Thus, to model a production system, functional models, which represent the different elements of the operative part of these system, are instanced from existing generic models and then are assembled for forming the complete model.<<ETX>>

Sizing, Cycle Time and Plant Control Using Dioid Algebra

Using an industrial process from the car sector, we show how dioid algebra may be used for the performance evaluation, sizing, and control of this discrete-event dynamic system. Based on a Petri net model as an event graph, max-plus algebra and min-plus algebra permit to write linear equations of the behavior. From this formalism, the cycle time is determined and an optimal sizing is characterized for a required cyclic behavior. Finally, a strict temporal constraint the system is subject to is reformulated in terms of inequalities that the (min, +) system should satisfy, and a control law is designed so that the controlled system satisfies the constraint.

Steady state of continuous neutral weighted marked graphs

Hybrid Petri Nets (PN), combining T-timed discrete PN and continuous PN, are convenient for the modelling and the performance analysis of fluid systems or manufacturing systems such as batch or high speed production systems. For instance, the continuous process can be modelled by a continuous PN while the state of machines, up or down, can be represented by a discrete PN. The aim of the paper is to characterise the timed dynamic behaviour of continuous PN with constant speed. More precisely, the final values of the instantaneous firing speeds of continuous neutral weighted marked graph, supposed live, are determined independently of the initial marking and without using the timed evolution. Finally an application to a flow system is given.

Final marking of continuous neutral weighted marked graphs

We consider continuous Petri nets that are used to model high throughput systems and flow systems. More advanced, continuous marked graphs are well adapted to model cyclic systems in a compact form. Nevertheless, to evaluate performances of continuous models, it is still necessary to study the evolution graph of the model. However, the determination of all the occurred events can be long and tedious. Therefore, this paper presents a new algebraic method based on the graph theory to determine the final marking vector.

Control of temporal constraints based on dioid algebra for timed event graphs

We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behavior only depends on the initial marking and on the control that is applied. As it is well-known, this behavior can be modelled by a system of difference equations that are linear in the min-plus algebra (/spl Ropf/ /spl cup/{+/spl infin/}, min, plus). The temporal constraint is represented by an inequation, that is also linear in the min-plus algebra. Then, a method for the synthesis of a control law ensuring the respect of the constraint is described. Two sufficient conditions are given, in terms of initial tokens and delays along the graph. We give explicit formulas characterizing a control law, which, if the conditions are satisfied, ensures the validity of the temporal constraints. This control law is also defined as a linear system over the min-plus algebra. It is a causal state feedback, involving delays. The method is illustrated on a production system.

Transitory state of neutral continuous marked graphs

Continuous Petri nets are available for the modelling of flow systems and discrete event dynamic systems with a large number of components. More advanced, when all conflicts are already solved, weighted marked graphs structure may be used. These graphs are elementary Petri nets where each place has exactly one input and one output transition and weighted are assigned to arcs. This paper concerns the characterisation of the transitory behaviour of flow systems modelled by neutral continuous marked graph.